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how to make a consolation draw?

i am organizing a tournament with 12 and 11 teams in two separate divisions. each division i want to have a 1st round consolation bracket for the 1st round loser. i am having trouble figuring out how to guarantee teams who has a bye in the 1st round a position in the consolation draw.

So for the team of 12, you will have a bracket of 16, with 4 people with byes. In consolation, you will have a bracket of 8 with 0-3 byes depending who moves on.

So for instance A gets a bye, B gets a bye, C gets a bye D gets a bye, E plays F, G&H, I&J, K&L. EGIK loses and will go to cons, A plays F, B plays H, C&J, D&L. So if A and C loses, they go to cons, while everyone else moves on. Then cons will have ACEGIK and then 2 of those 6 will have a bye. If just A loses and goes to cons, you will have AEGIK in cons where 3 teams have a bye and so on. I'm not quite sure that all made sense.

With 11 teams, bracket of 16, 5 teams will have 1st round bye. Cons will be bracket of 8 again. Also with 0-3 byes, depending who makes it on from after the bye round.

The good thing is that you can only go to cons after losing 1st match, otherwise if you were to allow people to go to cons from like QFs, then that get a little more confusing on how the consolation brackets work.